For a planar dielectric, the electric field approaches the equilibrium electric field exponentially with time t, i.e.
where τ is a time constant.
This is the same formula as for a planar capacitor. Where the electrical properties of the dielectric are constant across the material τ=e/σ where e is the dielectric constant. When the conductivity changes across a sample of thickness x, τ=e0 ò 1/σ(x) dx
In the case of a constant conductivity, Emax is proportional to the inverse of σ and therefore to τ. This indicates that only materials with long time constants are susceptible to hazardous levels of internal charging. Normally a time constant of 1 day or longer is associated with susceptible materials. τ is effectively the period over which electron fluxes are integrated by the material. Hence 1-day time averages of electron give sufficient temporal resolution when defining a hazardous internal charging environment.